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Chapter 2: Q22P (page 52)

Find each of the following in rectangular a+zb form if z=2-z3; if z=x+zy.

1z-1

Short Answer

Expert verified

The value for 1z-i is given below

1z-i=1+2i101z-i=x-y-1ix2+y-12

Step by step solution

01

Given Information 

The complex number is 1z-i.

02

Definition of the Complex number.

Complex number z can be written in the form of the real and imaginary numbers as:

z=a+zb

z=a+zb

Here z is the complex number, and a and b are real numbers

03

Find the value.

The complex number is 1z-1.

Find the values for 2-3i .

z=2-3i

1z-i=12-4i=12-4i×2+4i2+4i=2+4i4-4i2=1+2i10

Find the values for x+iy .

z=x+iy1z-1=1y-1i=1x+y-1×x-y-1ix-y-1i=x-y-1ix2+y-12

The value for 1z-1 is given below:

1z-1=1+2i101z-1=x-y-1ix2+y-12

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Most popular questions from this chapter

Express the following complex numbers in the x+iyform. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others—try it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

13.(i−3)31−i

Find the disk on convergence for each of the following complex power series.

∑n-0m(z-2+i)n2n

Follow steps (a), (b), (c) above to find all the values of the indicated roots -13.

Express the following complex numbers in the x + iy form. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others—try it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

17.1(1+i)3

Question. Express the following complex numbers in the form. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others—try it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

24. (1-i3)21(i-1)38
See all solutions

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